Design are one of the most attractive and commonly

Design of an Active Tunable Phase Shifter for Advanced Communication SystemsS. Al mokdad, R. Al jamal, R. Lababidi, M.Le Roy, A. Perennec.  Lab-STICC, UMR CNRS 6285, Université de Brest (UBO)-Ensta Bretagne, [email protected]@[email protected] [email protected] [email protected]—In this paper, an active phase shifter is designed based on non-Foster elements which behave as a frequency independent perfectly matched over a wideband frequency ranging from 1GHz to 4GHz. The main outcome of this study is to get a phase shift variation around 1800 while having a low insertion loss and minimum return loss in the considered band. The active phase shifter is based on a negative element, which is generated using Negative Impedance Converter (NIC) circuits, which convert load impedance into a negative impedance. However, it is shown that the actual realization of NIC leads to undesired parasitic resistance that has a significant effect on the performance of the phase shifter. Therefore, our proposed circuit is build up by simply cascading two different topologies of NIC circuit in a certain way to achieve a constant transmission phase (S21) with low insertion loss while being matched over the target frequency range.Keywords—negative impedance converter, non-foster elements. Introduction Analog phase shifters are one of the most attractive and commonly used electronics circuits in the radio transmitter and receiver chain, essentially for many radar systems that are based on phased array antennas for achieving electronic beam control of the phase signal from the radiating array elements. A lot of passive phase shifter had been designed during the last decades 1, but designing an active flat phase 1800 phase shifter that is matched over a wide bandwidth and with a minimum insertion loss is a special problem.This work focuses on designing an active tunable phase shifter that exhibits a frequency independent phase shift from 1GHz to 4GHz. The design relies on the use of non-Foster elements namely negative capacitors, which is generated using a negative impedance converter (NIC) circuit that has been discussed within the recent years 2. Moreover, two different configurations of NIC circuit 3-4, were theoretically analyzed and tested to achieve desired negative impedance. However, it is shown that this obtained negative impedance is not purely reactive and it comes with a parasitic real part that affects the performance of the phase shifter. Therefore, using a proper design can simply achieve our desired results. Based on that, our active phase shifter design is realized using NIC circuit, which is implemented in practice as a cross-coupled pair (XCP) of FET transistors. The structure of designing this proposed phase shifter simply consists of two identical capacitive ? circuits each consisting of two shunt capacitances (C) and a negative capacitance (-C) connected in series. In addition, the phase shift agility feature from 1GHz to 4GHz is controlled by biasing varactor diodes whose capacitance is varied by varying the controlled voltage.The paper is organized as follows: Section ? represent the topology and design of 1800 phase shifter with the help on non-Foster elements, Section ? represent the simulation of an active tunable phase shifter and also give a study on its stability and phase variation using a varactor, Section ? give an overall conclusion of the active tunable phase shifter. Topology and designTopology principleFirst of all, Fig. 1, shows a 2-port phase shifter circuit which is composed of three shunt capacitances (C1) and two negative capacitances (-C2) connected in series and there value is equal to (C1) and loaded at both ends with 50 ? input impedance. Fig. 1. 1800 phase shifter (a), its symmetric plane (b), the even-mode equivalent circuit(c) and the odd-mode equivalent circuit (d).The insertion loss can be calculated as follow 5:Where Zin,e is even input impedance and Zin,o is the odd input impedance, and we can easily calculate Zin,e, and  Zin,o  as follows.As a result, the phase of S21 is written as:      In addition, by substituting the real and imaginary part of S21 we get:            And it is worth noting that this equation gives 1800 of phase shift if the value of the capacitors are chosen to be equal to (C1 =C2 = 1pF)                                                                                                                                                B. Realization of a negative capacitanceA negative capacitance can be realized as NIC using a pair of transistors like (FETs) transistors as seen in the Fig. 2.Fig. 2. The topology of a negative capacitor using NIC. However, it can be noticed that NIC transform the load impedance to a negative impedance with a real part. Therefore, a study had been made on two type of NIC, namely NIC cross-coupled with output at the source and NIC cross-coupled with output at the drain so that we can eliminate the real part, and only left with a negative capacitance.In the real world, Field–effect transistors have parasitic effects, the capacitance in particular. Among these effects, only one of the main parasitic capacitance will be considered which the capacitance is across the gate and the source of the transistor (Cgs). Fig. 3, shows the NIC topology   Fig. 3. Equivalent simplified small-signal model of FET (a), equivalent        circuit of NIC output at source (b), equivalent circuit of NIC output at drain (c).The input impedance of the source and drain topology are calculated respectively as follows:As can be noticed that the input impedance consists of an imaginary part and a real part, but if we combine the two topologies together, that is if we cascade the source topology and the drain topology, we can get an input impedance with a real part equal to zero. The proposed topology is in Fig. 4.       Fig. 4. The proposed cascade topology of the phase shifter. After calculating the imaginary part of the cascade source and drain topology and putting it equal to -1pF, it is found that ZL for the source topology must be equal to a capacitance with a value of Cs = 1.18pF, and for the drain topology Cd = 2.36pF.Fig. 4, show the input impedance of the source topology and the drain topology NIC, compared with a capacitance of C= -2pF.Fig. 4. Zin1 represent the input impedance of NIC output at source compared to a negative capacitance of Zin = -2pF(a), Zin1 represent the input impedance of NIC output at drain compared to a negative capacitance of Zin = -2pF(b).As can be noticed that the real part of the source topology does not equal to the real part of the drain topology, meaning that if we cascade the two topologies in series, then the total real part will not be equal to zero, and this is a problem in a phase shifter, because it will lead to an insertion loss and the phase will not be flat. Therefore, we propose adding an inductance to the source topology, which will lead to a change in the real part of it, in order to be equal to the absolute value of the real part of the drain, and thus canceling it, leaving behind input impedance equal to -1pF. The proposed topology is shown in Fig. 5.Fig. 5. Modified NIC output at source (a), an equivalent circuit model of modified NIC output at source (b).The input impedance of the modified source topology is calculated and is given as follows:In order to have a real value which is equal to zero the value of inductance was calculated and chosen to be equal to 1.3nH, a comparison is made between the source and the drain topology in series, with the modified source topology in series with the drain, as seen in Fig. 6.Fig. 6. ADS schematic of the source topology cascaded with the drain topology (a), ADS schematic of the modified source topology cascaded with the drain topology (b).The total real impedance is measured in both cases and it is found out that the total real impedance is reduced to about zero using the modified topology of the source as seen in Fig. 7. Fig. 7. The real part of the source topology (red curve) and the drain topology (blue curve) and total real part of both topologies (purple curve) (a), Real part of the modified source topology (red curve) and the drain topology (blue curve) and total real part of both topologies (purple curve) (b).ACTIVE TUNABLE PHASE SHIFTER SIMULATIONThe simulation of the phase shifter is carried out with the modified cascade source-drain topology, as in Fig. 8, the input reflection coefficient (S11) and the forward transmission coefficient (S21), as well as the phase of S21, are depicted in Fig. 9, the value of the load capacitor at the source is Cs = 1.67pF and at the drain is Cd=2.36pF.Fig. 8. The Complete circuit structure of the active phase shifter.Fig. 9. The reflection coefficient and the forward transmission coefficient of the phase shifter topology (a), the transmission phase of the phase shifter topology (b).As can be noticed from the results, the phase shifter circuit exhibits a good performance within the frequency range of 1GHz to 4GHz with a good match and a low insertion loss of   -0.48 dB and a minimum return loss of -56 dB with a flat phase shift response of 1800.We had simulated the phase shifter using the model EC2612 package less FET, stability study have been taken into account while designing the network containing active components. The stability of the phase shifter was analyzed using the stability factor µ. Fig. 10, show the stability result, and as can be concluded, the device is unconditionally stable (µ > 1) over the frequency range from 1GHz to 4GHz.Fig. 10. The Mu stability factor of the phase shifter topology.We also vary the value of the capacitance in order to study the change in the phase, we chose three values for C1, that is C1= 1.03pF, C1=1.06pF, and C1=1.1pF, the result of the phase shift is given in Fig. 11.Fig. 11. Phase variation using a varactor.conclusionAn active tunable phase shifter that behaves as a frequency independent perfectly match with an 1800 phase shift from 1GHz to 4GHz has been proposed. The network consists of a three shunt capacitors and two negative capacitance connected in series. The negative capacitance has to be realized as a two negative impedance converter, namely NIC output at the source and NIC output at the drain, and are cascaded in order to have a real part equal to zero and an imaginary part equals to     -1pF. Stability study shows that the network in unconditionally stable over the frequency range of interest, and by using a varactor, we were able to change the phase of the inverter.Our next step is to build up the phase shifter, measure up the phase, the return and the insertion loss, in order to verify our design.References  G. Eason, B. Noble, and I.N. Sneddon, “On certain integrals of K. Khoder, M, Le Roy, A. Perennec ?An All-pass Topology to Design a 0-3600 Continous Phase Shifter with Low Insertion Loss and Constant Differential Phase Shifter?D. Kholodnyak, V.Turgaliev, A. Rusakov, K. Zemlyakov, I. Vendik “A frequency Independent Phase Inverting All – pass Network Suitable for a Design of Ultrawideband 180° Phase Shifters ”S. Saadat, H. Aghasi, E. Afshari, H. Mosallaei “Low – Power Negative Inductance Integrated Circuits for GHz Applications”, IEEE Microwave and Wireless Components Letters, VOL. 25, NO. 2, February 2015B. Razavi “The Cross-Coupled Pair – Part I”, IEEE Solid-State Circuits Magazine, 26 August 2014G.Hong, M.J.Lancaster, Kai Chang “Microstrip Filters for RF/Microwave Applications”, Series Editor